Colorado State Standards for Mathematics: Grade 7

CO.1. Number Sense, Properties, and Operations

1.1. In the real number system, rational numbers have a unique location on the number line. Students can:

1.1.a. Read, write, locate on number line, compare and order integers and positive rational numbers

1.1.b. Apply the definition of absolute value with integers, quantifying the distance from zero

1.1.c. Express large and small numbers using scientific notation

1.2. Formulate, represent, and use algorithms with integers and positive rational numbers flexibly, accurately, and efficiently. Students can:

1.2.a. Simplify numeric expressions using the order of operations

1.2.b. Add, subtract, multiply, and divide integers

1.2.c. Use mental math and estimation strategies to solve problems involving percents

1.2.d. Solve problems involving percent of a number, discounts, taxes, simple interest, percent increase, and percent decrease (PFL)

1.3. Proportional reasoning involves comparisons and multiplicative relationships among ratios. Students can:

1.3.a. Use ratio relationships to solve for a missing value in a proportion

1.3.b. Model proportional relationships with bar models, ratio tables, and similar figures

1.3.c. Explain the difference between a ratio, rate, and unit rate

1.3.d. Estimate and compute unit cost of consumables (to include unit conversions if necessary) sold in quantity to make purchase decisions based on cost and practicality (PFL)

CO.2. Patterns, Functions, and Algebraic Structures

2.1. Relationships involving the constant rate of change are modeled and solved using linear functions. Students can:

2.1.a. Given a linear situation (including direct variation), identify variables and write an equation in slope-intercept form

2.1.b. Given a linear equation (including direct variation), substitute input values to create a table and graph coordinate points in all four quadrants

CO.3. Data Analysis, Statistics, and Probability

3.1. Visual displays and summary statistics with one-variable data condense the information in data sets into usable knowledge. Students can:

3.1.a. Distinguish between median as middle number and mean as balance point for an ordered set of data

3.1.b. Use Mean Absolute Deviation (MAD) to analyze the spread of a set of data

3.1.c. Construct and interpret dot plots, histograms, stem-and-leaf plots, and circle graphs

3.1.d. Construct and interpret a box plot using the five-number summary and identify the interquartile range (IQR) for a set of data

3.1.e. Compare sets of data using shape (skewed, normal, uniform), with appropriate measures of central tendency (mean, median, mode), and appropriate measures of spread (range, IQR, MAD)

3.1.f. Given a frequency table, calculate relative frequencies

CO.4. Shape, Dimension, and Geometric Relationships

4.1. Objects in space and their parts and attributes can be measured and analyzed. Students can:

4.1.a. Develop and apply formulas and procedures for the surface area and volume of right cylinders and right prisms

4.1.b. Develop and apply formulas and procedures for area of regular polygons, circumference and area of circles, and area of composite figures

4.1.c. Identify and construct two-dimensional nets of prisms and cylinders

4.2. Proportional reasoning is used to make indirect measurements. Students can:

4.2.a. Describe the relationship between the circumference and diameter of a circle

4.2.b. Read and interpret scales on maps

4.2.c. Use proportions to convert from one set of units to another within customary and metric systems using standard units of measure for length, weight, capacity and time

CO.5. Prepared Graduate Competencies in Mathematics: The prepared graduate competencies are the preschool through twelfth-grade concepts and skills that all students who complete the Colorado education system must master to ensure their success in a postsecondary and workforce setting.

5.1. Understand the structure and properties of our number system. At the most basic level numbers are abstract symbols that represent real-world quantities

5.2. Understand quantity through estimation, precision, order of magnitude, and comparison. The reasonableness of answers relies on the ability to judge appropriateness, compare, estimate, and analyze error

5.3. Are fluent with basic numerical and symbolic facts and algorithms, and are able to select and use appropriate (mental math, paper and pencil, and technology) methods based on an understanding of their efficiency, precision, and transparency

5.4. Make both relative (multiplicative) and absolute (arithmetic) comparisons between quantities. Multiplicative thinking underlies proportional reasoning

5.5. Recognize and make sense of the many ways that variability, chance, and randomness appear in a variety of contexts

5.6. Solve problems and make decisions that depend on understanding, explaining, and quantifying the variability in data

5.7. Understand that equivalence is a foundation of mathematics represented in numbers, shapes, measures, expressions, and equations

5.8. Make sound predictions and generalizations based on patterns and relationships that arise from numbers, shapes, symbols, and data

5.9. Apply transformation to numbers, shapes, functional representations, and data

5.10. Make claims about relationships among numbers, shapes, symbols, and data and defend those claims by relying on the properties that are the structure of mathematics

5.11. Communicate effective logical arguments using mathematical justification and proof. Mathematical argumentation involves making and testing conjectures, drawing valid conclusions, and justifying thinking

5.12. Use critical thinking to recognize problematic aspects of situations, create mathematical models, and present and defend solutions